Does inequality really matter? The poor have what their grandparents would think unimaginable luxuries - TVs, telephones and washing machines. So why should it matter to them if in some unseen stratosphere the gated kleptocrats on company boards award themselves staggering sums of money? Does anyone really mind the gap?

That is a reasonable question and it niggles away at those on the left, too. Equality has gone out of fashion. Social justice under Labour means heaving the poorest over the poverty threshold and lifting the life chances of children from lower social classes. Tony Blair said early on that he was not bothered about wealth, only about abolishing poverty. Talk of inequality sounds like the old politics of envy. Equality of opportunity, yes, but equality for its own sake, why?

Here is the answer. Richard Wilkinson is a professor of social epidemiology, an expert in public health. From that vantage point he sees the world in terms of its physical and psychological wellbeing, surveying great sweeps of health statistics through sociological eyes. He has assembled a mountain of irrefutable evidence from all over the world showing the damage done by extreme inequality. However rich a country is, it will still be more dysfunctional, violent, sick and sad if the gap between social classes grows too wide. Poorer countries with fairer wealth distribution are healthier and happier than richer, more unequal nations.

This book is timely since the NHS annual report has just found that Labour has missed two key goals, both symptoms of inequality. Infant mortality and life expectancy figures are both moving in the wrong direction. If Labour is perplexed as to the reason why, Wilkinson can suggest plenty of answers here. Life expectancy in rich nations correlates precisely with levels of equality. So Greece, with half the GDP per head, has longer life expectancy than the US, the richest and most unequal country with the lowest life expectancy in the developed world. The people of Harlem live shorter lives than the people of Bangladesh. When you take out the violence and drugs, two-thirds of the reason is heart disease. Is that bad diet? No, says Wilkinson, it is mainly stress, the stress of living at the bottom of the pecking order, on the lowest rung, the stress of disrespect and lack of esteem. Bad nutrition does less harm than depression.

The book blisters with research like this: tests found that subordinate, low-status monkeys had high levels of the stress hormone, cortisol, which leads to arteriosclerosis. When the high-status monkeys were all put together and low-status monkeys put in another enclosure, all the pecking orders changed. When some previous high-rankers became subordinate they developed all the same physical symptoms, including a five-fold increase in arteriosclerosis within less than two years. Meanwhile, some of the low-rankers who suddenly found themselves dominant, had sharply dropped levels of stress hormone.

People, says Wilkinson, are the same. Social status and respect matter beyond anything, and the psychological damage done by being at the bottom is crippling. A survey of Whitehall civil servants found junior ranks were three times more likely to die in a year than seniors, with a fine sliding gradation from top to bottom according to status. If one office was found to be killing three times more than another next door, it would be evacuated instantly. Yet social environment may matter almost as much as asbestos.

Homicide rates (and other crimes) track a country's level of inequality, not its overall wealth. The fairest countries have the highest levels of trust and social capital. The American states that have the more equal income distribution also have most social trust: New Hampshire, the most equal, is least likely to agree that "most people would try to take advantage of you if they got the chance".

Wilkinson's message is that social environment can be more toxic than any pollutant. Low status and lack of control over one's life is a destroyer of human health and happiness. The wealth gap causes few to vote or participate in anything in a world of fear, conflict and hostility.

It is not primarily five-a-day fruit and veg or obesity that need targeting, but social injustice itself. Infant mortality is mainly a result of low-birth weight babies, something the government has tried hard to improve. Wilkinson shows that these days small premature babies are not caused by bad diet: even poor nutrition by British standards will rarely harm a foetus. It is stress in pregnancy that does it, high cortisol levels which affect the foetus for life - and poorer mothers are more depressed, with less social support. Psyche matters more than vitamins, all through life. An orphanage in hungry post-war Germany found children on the same diet were found to have grown most under the kindest matron and least under the unkindest matron.

Poverty in rich nations is not a number or the absence of a particular necessity. A poor vicar may bring up children well on lentils and respect. But for most people respect is measured in money. Low pay tells people that their labour and they themselves are worth little. Poverty is not, as the government imagines, a line to pull people over but it is a position on a line. If it tilts too sharply upwards, the pain of those at the bottom can be measured in hard statistics.

This book is evidence for what common sense already knows. Children on free school meals, with no holidays to talk about, unable to afford the school trips, who never invite anyone back to a shabby home, painfully understand their place in the hierarchy from their first day at school. Adults know the same, noses pressed up against the window of lifestyle shows on TV. This is a book that puts the numbers to a psychological truth: inequality is the real enemy.